ABSTRACT

We study a family of type II multiple orthogonal polynomials. We consider orthogonality conditions with respect to a vector measure, in which each component is a q-analogue of the binomial distribution. The lowering and raising operators as well as the Rodrigues formula for these polynomials are obtained. The difference equation of order r + 1 is studied. The connection via limit relation between four types of Kravchuk polynomials is discussed.

中文翻译：

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多个 q-Kravchuk 多项式

摘要

我们研究一族 II 型多重正交多项式。我们考虑关于向量测度的正交条件，其中每个分量都是二项式分布的q类比。得到了这些多项式的降和升算子以及罗德里格斯公式。 研究了r +1阶差分方程。讨论了四种Kravchuk多项式之间通过极限关系的联系。